* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr June 3 (Reuters) - Euro zone bond yields clung near recent lows on Thursday after further dovish commentary from ECB President Christine Lagarde, while focus was squarely on data and central bank speakers in the United States. The European Central Bank will support the euro zone “well into” its recovery from a pandemic-induced double dip recession, Lagarde said on Wednesday. With that ECB policymakers entered their silent period on Thursday, a week before their policy meeting on June 10, where they avoid saying anything that could influence expectations about monetary policy decisions. Comments they made in recent weeks, led by Lagarde, that it would be too early for the ECB to discuss slowing its pandemic emergency bond purchases (PEPP) helped reverse a sharp sell-off in the bloc’s government bonds in May. Yields have held in a relatively tight range for the last week. Germany’s 10-year yield, the benchmark for the bloc, was up less than a basis point by 0758 GMT, at -0.19%, similar to most other 10-year yields in the bloc. Italian 10-year yields were unchanged at 0.88%. “The key pointers for the (euro government bond) market near term is tomorrow’s U.S. labour market report and the ECB meeting on next Thursday,” said Piet Christiansen, chief strategist at Danske Bank. Data due at 1230 GMT is expected to show weekly U.S. jobless claims decreased, while a private employment report is set to point to a slightly lower increase than in April, according to Reuters polls, setting up markets ahead of the closely watched non-farm payroll data due Friday. U.S. data releases often move euro area bonds in tandem with U.S. Treasuries, as the two debt markets are closely correlated. Focus will also be on U.S. Federal Reserve speakers on Thursday, after policymaker Patrick Harker said it may be time for the bank to start thinking about the best way to slow the pace of its asset purchases - adding to an emerging shift in tone from policymakers, who until recently said it was too early to contemplate the discussion. In the primary market, investors will be eyeing longer-dated supply, with Spain set to auction bonds due as long as 2040 and France expected to raise up to 11 billion euros from an auction of long-dated bonds due as long as 2072. (Reporting by Yoruk Bahceli Editing by Shri Navaratnam) Our Standards: The Thomson Reuters Trust Principles.